The American Mathematics Competitions (AMC) is a series of high school mathematics contests used to select the six-member team to represent the United States at the International Mathematical Olympiad (IMO).
There are certain rewards for doing well on the AMC tests. For the AMC->8, a perfect score may earn a book prize or a plaque (as it did for the students who achieved perfect scores in 2002); a list of high scoring students is also available to colleges, institutions, and programs who want to attract students strong in mathematics. This may earn a high scorer an invitation to places like Math Path, a summer program for middle school students. The top-scoring student in each school is also awarded a special pin.
For the AMC->10 and AMC->12, a high score earns recognition (in particular, perfect scorers' names and pictures are published in a special awards book); as with the AMC->8, a list of high-scoring students is also available to colleges, institutions, etc. The top-scoring student in each school is awarded a special pin, or a bronze, silver, or gold medal, depending on how many times he or she was the top scorer. For more information on awards, visit Awards for the AMC.
In addition, high scorers on the AMC->10 and AMC->12 qualify to take the next round of competitions, the 3-hour long American Invitational Mathematics Examination (AIME), typically held in March or April. Any student who scores in the top 1% on the AMC->10, scores in the top 5% on the AMC->12, scores at least 100 points on the AMC->12, or scores at least 120 on the AMC->10 is invited to take the AIME. The answer to each of the 15 questions on the AIME is an integer between 0 and 999 inclusive, so while it is technically a multiple-choice test, it is not one in practice.
The combined scores of the AMC and the AIME are used to determine those that will be invited back to take a grueling 9-hour, 2-day, 6-problem session of proofs known as the United States of America Mathematical Olympiad (USAMO). Approximately thirty students are selected based on their USAMO performance to be trained at the Mathematical Olympiad Summer Program, or MOSP (better known as MOP to its participants). In addition, in 2004, twenty-five 9th grade students were selected to participate in MOSP.
During this summer camp, a series of exams are given to finally pick the 6 member US Mathematics Team. The current coaches of the US Math Team are Titu Andreescu, director of the AMC, and Zuming Feng, from Phillips Exeter Academy.
Website: www.unl.edu/amc/